Density functional theory methods have been used to investigate the effects of adding one to four protons to a one-plane guanine quartet (G4) and a two-plane guanine quartet stack (2G4). The singly protonated G4 complex prefers protonation at the Watson–Crick face of the O6 moiety. However, all multi-protonated G4 complexes favour protonation at the Hoogsteen face of the O6 centres. The proton affinities have also been calculated for the addition of one, two, three and four protons to the central oxygens of G4 and have been compared with those of monomeric guanine and other biochemically appropriate bases. These results suggest that a G4 might reasonably readily accept two protons. For the singly to quadruply protonated 2G4’s, the added protons prefer to distribute over both planes with maximally two per plane. Furthermore, unlike the (G4-nHnH⁺+) n≥ 2 complexes, protonation at the Watson–Crick faces of the O6 moieties is found to be preferred for all protonation states. In addition, (2G4-nHnH⁺+) n = 1–4 complexes were also obtained in which inter-plane hydrogen bonds were formed, effectively enabling the protons to ‘sit between’ planes.